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A Running Gag in the Adrian Mole books is self-proclaimed intellectual Adrian completely missing the point of whatever book he's reading. For instance, after finishing Animal Farm he declares "From now on I'm treating pigs with the contempt they deserve. I am boycotting pork of all kinds."
A conversation in Adventures of Huckleberry Finn between Huck and Jim: they are discussing historical kings, and when Huck brings up King Solomon, Jim goes on a rant about how foolish it is to split a child in half to settle a custody dispute. Nevermind that it was an obvious bluff, and the real mother would give up the child to save its life. Huck calls him out on this, saying "You missed the point by a thousand mile". (Given how Huck explains the judgement and given how he seems unable to give an explanation beyond "You just don't understand!", one almost gets the implication that Huck himself doesn't quite grasp the point.)
Angela and Diabola: When Diabola first enters school at the age of six, she draws a number of extremely disturbing pictures involving people dying horrible deaths. Her principal praises the pictures and labels Diabola an artistic genius, while completely failing to grasp her obvious violent and sociopathic tendencies.
In Bride of the Rat God, Christine hears her Prima Donna Director call people Philistines for trying to ruin his vision, she thinks he means Philistines in the film, where there were only supposed to be Persians.
Elizabeth Bathory in Count and Countess thinks she's being generous when she offers to let her closest servants have a nice, relaxing dip in her Blood Bath. She doesn't understand why they hastily decline.
In the Tiffany Aching subset of Discworld books, Tiffany's father takes great care to keep the clock on the mantelpiece set properly. He does this by looking at the clock tower in town each time he visits the market, remembering how it looked all through the slow, miles-long trek home, and then adjusting the Achings's clock to match what he'd seen. (It's mentioned that, since he gets up at dawn and works until it's dark, it doesn't really matter what time it is, but then, why try to set it at all?)
A running gag in The Amazing Maurice and His Educated Rodents is that some of the more thoughtful rats think you shouldn't eat other rats. The more practical rats think this is sound advice: obviously you shouldn't eat a dead rat until you know what it died of, and you certainly shouldn't eat the green wobbly bit.
Here's an exchange between Vetinari and Colon in Jingo, the latter obviously having never heard of a firing squad:
'I should imagine they'd give you a cigarette.'
'A cigarette?' said Fred.
''Yes, sergeant. And a nice sunny wall to stand in front of.'
Sergeant Colon examined this for any downside. 'A nice roll-up and a wall to lean against?' he said.
'I think they prefer you to stand up straight, sergeant.'
'Fair enough. No need to be sloppy just because you're a prisoner.'
Inverted in Going Postal Moist, when inquiring about the location of the Post Office's two missing chandeliers, he is told by a wizard they are currently in the Assassins' Guild and the Opera House. It's Moist himself who doesn't understand the assassins only ever kill for money.
Moist: Yes, I think I shall put that off for a day or two, dangerous people to tangle with.
Wizard: Indeed. I understand some of those sopranos can kick like a mule.
Divine Diva by Daniel Gagnon. The famous singer Iolanda is dying; the President, corrupt head of a corrupt and crumbling government, repeatedly calls her, pleading with her to return to the stage and revive both of their glory days, and making a thousand excuses as to why the political situation isn’t his fault. Iolanda tells him she’s rejected her earlier life of hedonism and extravagance and at last found love, in the person of Francesca, the humble young woman who cares for her. Francesca bluntly tells the President his faults. The President, denied Iolanda by death, tries to instead win over Francesca, but without ever admitting wrongdoing: having completely missed the point of what Iolanda values in her, he tells her that he’ll gladly listen to her talk of corruption and starvation if she’ll only have dinner with him at a fancy restaurant. He gets the only possible response when Francesca hangs up on him.
Deuce of Edenborn is a bit of a Pyro Maniac, so it's reasonable that his father warns him about fire safety before sending him to meet his cousins. Therefore Deuce is careful to stamp out fires caused by the explosives he slings throughout their house.
Bartimaeus: Two measly human years to get over the trauma of meeting you. Sure, I knew some idiot with a pointy hat would one day call me up again, but I hardly thought it would be the same idiot as last time!
In High Fidelity, Rob tries to figure out what his ex meant when she said she hadn't had sex with her new boyfriend yet, and asks a friend for help figuring it out with a different example. It doesn't go well.
Rob: What would it mean to you? That sentence? "I haven't seen Reservoir Dogs yet?" Barry: To me, it would mean you're a liar. Either that or you've gone potty. You saw it twice. [snip] Rob: Yeah, yeah, I know. But say I handn't seen it and I said to you, "I haven't seen Reservoir Dogs yet," what would you think? Barry: I'd think you're a sick man. And I'd feel sorry for you. Rob: No, but would you think, from that one sentence, that I was going to see it? Barry: I'd hope you were, yeah, otherwise I would have to say that you're not a friend of mine.
''Missing the point with all the futile diligence of a blind machine-gunner."
Subverted by the antique-shop owner in the Maggody mystery novels, whose sign ("Antiques: New and Used") seems like this trope, but is actually Obfuscating Stupidity employed to lure in gullible tourists.
In Malevil: Big Bad Fulbert of La Roque and The Hero Emmanuel of Malevil are having a pissing contest over who has authority in the region after World War III. Religion is their primarily weapon, Fulbert appoints himself priest of La Roque and so Emmanuel is elected as priest of Malevil. When Fulbert announces he is appointed as Bishop, Emmanuel decides to respond with sarcasm and his own ridiculous claim. He digs out six hundred year old documents from the Hundred Years War claiming that the Lord of Malevil is Feudal Overlord over La Roque, with power over the clergy, and that he inherits the title and power by virtue of owning the property before the war. His friends unfortunately rally under the idea that they now have the "legal" right to overthrow the evil priest.
The Mortal Instruments: More than once during an Anguished Declaration of Love, where Alec Lightwood seems more concerned with the fact that Magnus didn't return his calls and lied about his age than the fact the city is under attack and Magnus is explaining all the pain Alec's closeted-ness and his love is causing him. Leading us to this little gem where they BOTH end up missing the point of their conversation:
"You told me you were three hundred! You're seven hundred years old?"
"Well, eight hundred, but I don't look it."
In James Thurber's short story "Mr. Preble Gets Rid of His Wife," Mr. Preble is planning to murder his wife so he can run off with his secretary. She is suspicious when he asks her to go down to the cellar with him, and he blurts out the truth almost immediately — and ends up in an argument about the selfish and inconsiderate way he's chosen to go about it (she's in the middle of a book and doesn't feel like going down to the cellar to be murdered just now; it's cold down there, and he's picked out a lousy murder weapon and makes her wait while he goes to find another one... and so on).
Croup seems to be disappointed about not hitting any fingers, implying that he couldn't even tell the difference.
New York magazine used to have various humorous reader competitions. One of them was to write literature and theater reviews as if by a critic who Completely Missed The Point. (E.g., one entry panned Crime and Punishment for revealing the murderer's identity at the beginning, thus spoiling the mystery. Another reviewed a Dick and Jane book, saying that the author seems to be aiming for a Hemingway-like style, "but the effect is mechanical rather than taut.") This may have been inspired by a genuine review of Lady Chatterlys Lover published in a country sports magazine, which complained that all the interesting parts about the life of a gamekeeper were broken up by a tedious romantic subplot.
Lydia and Mrs. Bennet from Pride and Prejudice are both thrilled with Lydia's Shotgun Wedding to Mr. Wickham, in spite of the fact that Wickham ran off with Lydia for two weeks with no intention of marrying her and left a pile of debts behind him, making it clear that he's horrible husband material by any standard of the time. Mrs. Bennet at least is upset about the situation until the marriage is confirmed, and has good reason to be relieved that her daughter (and by extension the prospects of all her other daughters) is not Defiled Forever, but it never even occurs to Lydia for a moment that she's done anything to be embarrassed about, and she first smugly congratulates herself for the great joke she's playing on everyone by running off with the man, then later badgers her sisters to congratulate and praise her for her marriage.
In The Screwtape Letters, the eponymous demon explains to his nephew that, since there is of course no such thing as real love, God cannot possibly really love humanity, and therefore His professed love must be some kind of elaborate deception in order to preserve His power, and that if only the forces of Hell could figure out the scheme behind this deception, they could succeed in winning their war with Heaven:
Screwtape: Since then, we have begun to see why our Oppressor was so secretive. His throne depends on the secret. Members of His faction have frequently admitted that if ever we came to understand what He means by Love, the war would be over and we should re-enter Heaven. And there lies the great task. We know that He cannot really love: nobody can: it doesn't make sense. If we could only find out what He is really up to!
When Shamisen the calico cat suddenly speaks (with with the voice of an old philosopher) in The Sighs of Haruhi Suzumiya, Itsuki is first surprised that it's a male calico. Lampshaded by Kyon.
In Surely You're Joking, Mr. Feynman!, Richard Feynman describes his experiences with physics education in Brazil. For example, students knew cold that "Brewster's Angle is the angle at which light reflected from a medium with an index of refraction is completely polarized." They knew that the light is polarized perpendicular to the plane of reflection. They even knew that the angle's tangent equaled the index of refraction. But when Feynman told them to look out over the water — nothing. When they looked through polaroid, they gushed "Ooo, it's polarized!"